1. Field of the Invention
This invention pertains generally to diagnostic and interventional imaging using beams and detectors, and more particularly to systems and methods for creating a three dimensional cross sectional image of an object by the reconstruction of its projections that have been iteratively refined through modification in object space and Fourier space.
2. Description of Related Art
Tomography is an important diagnostic and interventional tool in medicine, biology, geophysics, materials science, archeology, astronomy and the other sciences. It is an imaging technique that produces a cross sectional 2D or 3D image of the internal structures of an object from its projections. The typical tomography apparatus contains a radiation source and a detector that is rotated around an axis extending perpendicularly from the plane of the examination table. Projections of the patient or object are conventionally taken at equal angle intervals such that the angle of the radiating source with respect to the isocenter of the scanner changes by a fixed amount from one projection to the next. Images have been produced from several different beam sources including x-rays, electrons, gamma rays, ions, neutrons, sound waves and others.
A central problem in tomographic imaging is the radiation dose that is directed to the patient or biological specimen as the result of the imaging procedure. With the increasing popularity of medical x-ray CT and fluoroscopic interventional imaging procedures, the long term effects of exposing patients to such ionizing radiation is of increasing concern, especially for pediatric patients. An additional problem in tomographic imaging is the degradation of resolution and other image quality parameters due to the problem of missing or incomplete sets of projection data. Missing projection data can arise from radiation dose restrictions or from practical mechanical limitations in the imaging procedure or imaging system. One example is the missing wedge problem that occurs in electron microscopy, i.e., specimens cannot be tilted beyond ±70° and the data in the remaining ±20° projections are missing. These difficulties currently limit the resolution of the 3D imaging of cellular and organelle structures.
In addition to the problems of radiation dose and missing projection data, conventional image reconstruction algorithms suffer from inaccuracies from interpolation limitations. Conventional tomography reconstructs a 3D object from a set of equally angled 2D projections. The manner of acquisition inherently forces the projection data into a polar format. Since the set of projections are in polar coordinates and the object is in Cartesian coordinates, interpolation has to be used in the reconstruction process either in object space or Fourier space. Such interpolations may account for a large source of error from the reconstruction algorithm alone and result in a significant degradation of image quality as measured by the resolution, contrast, and signal to noise ratio.
Currently, the most widely used slice reconstruction algorithm is the filtered back projection (FBP). The filtered back projection scheme is computationally fast, but does not offer any solutions for the problem of excessive radiation dose exposure and the problem of image degradation due to missing projection data. In addition, FBP suffers from inaccuracies due to inherent interpolation problems that occur in the back projection process. As a result of the problem of missing projection data and the problem of interpolation, images reconstructed with the FBP method often contain artifacts that degrade the resolution and overall image quality.
In addition to FBP, other reconstruction algorithms exists that are not in general use because they are computationally expensive under practical imaging conditions and also suffer from the problem of interpolation, which reveals itself when the forward projection process is modeled into the system matrix. These methods are also very sensitive to experimental noise and often diverge under realistic noisy experimental situations if the noise is not correctly modeled into the algorithm.
It can be seen that, reconstruction algorithms currently existing in the art, such as Filtered Back Projection, are not mathematically exact and consequently may produce images of lower resolution, contrast, and signal to noise ratio than what may be possible. These introduce inherent errors in the reconstructed image that result primarily from the reconstruction algorithm itself as opposed to experimental error. Furthermore, due to this degradation of image quality, conventional methods of tomography require a high dose of radiation to be administered to a patient to produce suitable images. Consequently, conventional methods have a significantly higher probability of inducing secondary effects such as radiation damage or carcinogenesis to the patient.
There is a need for a system and method for tomographic imaging that limits the exposure of the subject to potentially harmful or destructive radiation that is at the same time accurate, reliable and computationally practical. The present methods satisfy these needs, as well as others, and are generally an improvement over the art.